# Full text of "Mathematical And Physical Papers - Iii"

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```102
OX  THE  COLOURS  OF  THICK  PLATES.
focus, tlie difference of retardations of two waves starting from L and Ly and reaching the same given point.    Then
R = ( L to 4) + PM - PLB - {(M to M,) + PL - PMJ =
when*
r == />J/    / Y,3 - ( />/, - Ply = V - V", suppose.
According to the* explanation given in the preceding article, when the position of /> changes JiT remains constant, to the degree of approximation which it is proposed to employ, but the value of V depends upon tin* position of P. We have
and ;:     b>,(-/> '"'^'//"^ nearly.    Expanding, we get
r'     r. :   I'/ j   Irf/', when4   [r./ is the  sum of the terms ' ^ and j\ an«l  1' the sum of the terms containin    6 and
!4M M.ic;i jt.n t«> wriir down  [r|/f', since it, maybe deduced
f»;< v, i:?iir/ A, // for r/, ,/•.    Taking  lrr to denote for I7" what
:«"   !-I   I", we  '^'t't   h\   inteH'hanging r/ and a/, r/,} and a<t',
jd.T fl.-i"  ?^r rin.ijs mav he formrd on a screen with perfect
fi«         ;T   ;     in-eiv-.-arv   thaf   flu-   diilercnee  of   phase   of  the
p,t;i    .»!    rn-ams which coine from the several points of the
i     'n'.jV'    . ii-Hild   he   ihc same;  in   other   words, that  the
*!"!.   //    ii'ttjld  he   indepriident  of ,/• and //.     Deierring for
* u' ?li«- in?»«->.fixation «>f the conditions of distinctness, we
.-! .- 'I.-,-f v, hen these conditions are satisfied the expression```